Intereting Posts

If $(x_n)$ is a Cauchy sequence, then it has a subsequence such that $\|x_{n_k} – x_{n_{k-1}}\| < 1/2^k$
Recursive formula for variance
Divisibility criteria of 24. Why is this?
Discrete non archimedean valued field with infinite residue field
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
Why do negative exponents work the way they do?
Find all such functions defined on the space
Fractional Trigonometric Integrands
How can some statements be consistent with intuitionistic logic but not classical logic, when intuitionistic logic proves not not LEM?
Group of order 24 with no element of order 6 is isomorphic to $S_4$
Hatcher Problem 2.2.36
What interesting open mathematical problems could be solved if we could perform a “supertask” and what couldn't?
The space $C$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
Trigonometric substitution and triangles
Filling the gap in knowledge of algebra

In exercise 1.8 of chap I in Hartshorne algebraic geometry,

Let $Y$ be an affine variety of dimension $r$ in $\mathbf A^n$. Let $H$ be a hypersurface in $\mathbf A^n$, and assume that $Y \nsubseteq H$. Then every irreducible component of $Y \cap H$ has dimension $r-1$.

I refered to a solution.

In this solution, why $f$ is not a unit in $B$?

- proof of the Krull-Akizuki theorem (Matsumura)
- Isomorphisms (and non-isomorphisms) of holomorphic degree $1$ line bundles on $\mathbb{CP}^1$ and elliptic curves
- the fundamental exact sequence associated to a closed space
- integral cohomology ring of real projective space
- Vakil 14.2.E: $L\approx O_X(div(s))$ for s a rational section.
- Number of points at which a tangent touches a curve

- Neat way to find the kernel of a ring homomorphism
- There exists a unique isomorphism $M \otimes N \to N \otimes M$
- Localization of a ring which is not a domain
- A sufficient condition for a domain to be Dedekind?
- Infinite linear independent family in a finitely generated $A$-module
- Quotient ring of a localization of a ring
- Are there any commutative rings in which no nonzero prime ideal is finitely generated?
- Fields finitely generated as $\mathbb Z$-algebras are finite?
- What is the equation describing a three dimensional, 14 point Star?
- projective cubic

Let $H = Z(f)$ where $f$ is irreducible. Let $Y = Z(\mathfrak a)$ where $\mathfrak a$ is a prime ideal. Let $\overline f$ be the image of $f$ in the integral domain $B = A / \mathfrak a$. Every irreducible component of $Y \cap H$ corresponds to a minimal prime ideal of $B$ that contains $\overline f$. If $\overline f$ is a unit, no such prime ideal exists. Thus $Y \cap H = \varnothing$ and the given statement is vacuously true.

- What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
- Proof By Induction – Factorials
- Counterexample of polynomials in infinite dimensional Banach spaces
- Configuration scheme of $n$ points
- Possibility to simplify $\sum\limits_{k = – \infty }^\infty {\frac{{{{\left( { – 1} \right)}^k}}}{{a + k}} = \frac{\pi }{{\sin \pi a}}} $
- Enough Dedekind cuts to define all irrationals?
- Is every Lebesgue measurable function on $\mathbb{R}$ the pointwise limit of continuous functions?
- Is there a simple method to prove that the square of the Sorgenfrey line is not normal?
- Induction without a base case
- A Lebesgue measure question involving a dense subset of R, translates of a measurable set, etc.
- Is this urn puzzle solvable?
- Two curious “identities” on $x^x$,$e$,and $\pi$
- How does one prove that a multivariate function is univariate?
- Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?
- solve a trigonometric equation $\sqrt{3} \sin(x)-\cos(x)=\sqrt{2}$